can't get same results Matlab generates

Question

Take a look at the following transfer function:

With Matlab Simulink:

The result is

In State-space representation, the system can be modeled as follows:

In Matlab, we can model the system in the state-space representation:

which yields the following plot:

which is exactly the result generated by using transfer function. I'm trying to generate same results with odeint but failed. This is the code

#include <iostream>
#include <Eigen/Dense>
#include <boost/numeric/odeint.hpp>
#include <iomanip>
#include <fstream>


using namespace std;
using namespace boost::numeric::odeint;

typedef std::vector< double > state_type;

void equations(const state_type &y, state_type &dy, double x)
{
    Eigen::MatrixXd A(3, 3), B(3,1);

    /*
        x = y[0]
       dx = y[1] = dy[0]
      ddx = y[2] = dy[1]
     dddx =        dy[2]

    */
    const double r(1);

    A <<   0,   1,  0,
           0,   0,  1,
         -24, -26, -9;

    B << 0, 0, 1;      
    //#####################( ODE Equations )################################
    Eigen::MatrixXd X(3, 1), dX(3,1);
    X << y[0], y[1], y[2];
    dX = A*X + B*r;

    dy[0] = dX(0,0);
    dy[1] = dX(1,0);
    dy[2] = dX(2,0);
}


int main(int argc, char **argv)
{
    const double dt = 0.01;
    runge_kutta_dopri5 < state_type > stepper;

    state_type y(3); 
    // initial values
    y[0] = 0.0; //  x1 
    y[1] = 0.0; //  x2
    y[2] = 0.0; //  x3

    ofstream data("file.txt");

    for (double t(0.0); t <= 5.0; t += dt){
        data << t << " " << 2*y[0] << " " << 7*y[1] << " " << 1*y[2] << std::endl;
        stepper.do_step(equations, y, t, dt);
    }

    return 0;

}

And this is the result for all state vector

None of the preceding variables match the results generated by Matlab. Any suggestions to fix this code?

Jacob Jacob · Accepted Answer · 2017-10-25T20:57:31

Look at the expression you have for y. When you multiply a 1x3 matrix with a 3x1 matrix, the result should be a 1x1 matrix, where the value of the single element is the dot product of the two matrices. What you're currently doing is element-wise multiplication when you write to data instead of calculating the dot product.

can't get same results Matlab generates

1 Answers